Overall, vaguely, manpower bleed is you losing models/units in excess to your opponent. It's also, in general, the manpower spent on reinforcing squads, rebuilding lost units, or structures (bunkers, fighting positions, caches, etc.) lost. Those are, I think, the two ways that it can be defined.
Manpower bleed is one of the issues that, in the long term, contribute to defeat and, more often than not, don't win games decisively.
Manpower bleed is important in the game because the player that is suffering from it most is required to
1) spend more resources on being combat-effective/maintaining territory (ergo generating resources)
2) wait before reaching the next tech level
There are other things that result from mp bleed (a snow-ball effect, if you will) and are more esoteric or harder to define; there's the psychological aspect of losing more engagements (which is a typical indicator of manpower bleed) and being "outplayed"; there's the veterancy effect where your opponent's squads get veterancy faster because giving damage gives more xp than taking it; there's VP drain.
Preserving your manpower is important almost always
1) Retreating from an unwinnable fight is almost always recommended. Some exceptions include
a) to prevent the capture/decapture of a point
b) to capture a point (usually a vp, especially early game)
c) attempting to kill an enemy unit (usually a vehicle)
2) Preserving manpower is important because it prevents you from taking unnecessary losses.
Sure, you will lose engagements here or there, but if you trade more or less equally then you should be in a good spot, even if you lose a territory point. It's almost always better to wipe a squad and lose a point than lose a squad and hold a point (the very late game, of course, or where VPs are low for either side are some clear and constant exceptions).
Causing manpower bleed
I've always thought of manpower bleed in the way I've talked about it above. To me, it comes down to winning engagements. There are some ways to do that:
a) be behind superior cover at the most advantageous range
b) be behind equal cover at the most advantageous range
c) create your own cover
d) deny your enemy cover
i) put mines behind cover!
ii) use flamethrowers — they even have damage buff vs. heavy cover
iii) use indirect fire — green cover modifier applies from where the unit that fired the round comes from (it's advantageous to flank with a mortar squad...which doesn't really make sense but that's how the game works. But don't flank with a mortar squad).
2) minimizing your opponent's damage output
Basically, I've thought about this from the early game perspective of Wehrmacht and Soviets: Basically, you want to employ MGs or a sniper to increase the likelihood of you winning an engagements by reducing your opponent's DPS. MGs suppress and pin (reducing and eliminating damage, respectively) whereas snipers carve off a portion of DPS with every shot that connects.
3) building mines
mines win games. Apart from taking out key units, they render others less effective in combat and require players to reinforce their squad, also spending manpower. The Soviets have a distinct advantage in this regard because they have multiple infantry squads that can lay mines. While they don't have the advantage of having AT mines, their general purpose mine is good because it will hit anything. The trip wire flare is good (that's why it's had a lot of nerfs). They used to have an even larger advantage with demos, where a mine + demo combo could take out anything up to and including a Panzer IV.
4) Using vehicles
Vehicles take HP damage in exchange for dealing manpower damage (whenever a model is killed). Getting a scout car as whatever faction may be good not even for the purpose of killing units but for the tactical abilities it gets (which is an added bonus and not really necessary for the point I'm making). It also may force your opponent to heavily invest in anti-tank units which may play into your favor because they have one unit taking up popcap (and also manpower income) on a unit that is a hard counter to just one minor, annoying unit.
A good way to spend excess manpower is to build a cache. Typically, a munitions cache is the most useful as good unit preservation leads to mass amounts of fuel buildup over time. You can also get a second (although probably not a third) engineer squad to provide some utility and, perhaps, repair vehicles if you find yourself with a lot of them! The ability for extra utility (extra sweeper/flamer/AT/CQB squad) is great.
Mortars are great if you can find the time and the use. Against squads that need to stay in cover to be combat effective (ostruppen, infantry sections, etc.) they can be useful. Friendly fire is also a confusing issue but I do not think that mortars cause much damage to your own soldiers so, even in the event of a rush, mortaring your own squad isn't too bad. Mortars are also good for their smoke. You can smoke any long range unit/squad whether it be AT, an LMG squad, or an MG, it will surely help. It can also cover retreating units/tanks with smoke. The US have the advantage of having WP on some of their units which does damage and makes mopping up on retreat much easier.
Manpower bleed is something, like all parts of this game, easy to quantify the direct cost of but also contributes to many other things. It's easy (in theory) to look at the models killed and tally up the manpower lost. But other factors such as the cost of teching up, the loss of territory, the loss of VPs, the loss a key vehicle or squad, etc. are all factors that mp bleed takes into account. There are other factors, too, like army composition and manpower upkeep to consider too.
I still remember a game I played where I never lost much of my army and there was never one single point where I lost everything. I just got outplayed and bled out, unable to hold ground, unable to tech up. I just got outplayed and out-bled.
When watching casts of games, it's often easy to tell who's winning. Often times MP bleed is a result of players continually losing engagements so, when you're spectating, it can be easy to see who is winning and who isn't. Sometimes, though, there is a dramatic reversal and the game gets turned on its head. This can also be attributed to MP bleed in the early/mid game when a player gets out a light vehicle or medium tank and there is no contest on the field. Sometimes, sure, it's a strategic mistake by a player that decided to over-invest in a tier or get something they didn't need, but often times that first light vehicle is decided by map control or heavy MP losses that made getting a vehicle an impracticality for the not-so-visibly losing player.