Tripwire bombs are weapons that takes getting used to to be effective. There are very few instances where using it would be better than using different bomb type. It takes planning and patience and can be tough to use if you don't have either.
Tripwire bombs must be set by you so it may arm itself. To set it, you have to hold the bomb button down until you place it down. When armed, any NPC that walks within its triggering range will detonate it, that includes any unintended civilian NPC's that happens to walk by.
There are two rings visible when you set it. The innermost ring shows the triggering range and the outermost ring shows the explosion range. Any non-allied NPC that steps into the triggering range will detonate it while anyone within the explosion range will be affected by the bomb.
They are most useful if you have a target that is walking in a path that you know they will take. You can set the bomb along that path to hopefully get them. Most enemy NPC's that you will see in the game will have a particular patrol route. You can see if they have one by going into Eagle Vision to see it. The lines on the ground are the paths they will take and the circles in the paths indicate where they usually stop. Otherwise if your targets don't have a patrol route, you will have to anticipate where they will be moving.
They can also be used defensively. If you plan on getting into trouble, you can set some in a remote location where nobody will normally traverse and use them as your escape route. If you have any guards chasing you, lead them to your bombs. You will not set them off but your pursuers will.
You're not missing out on much IMHO, the other shells are far more useful since setting the trap is not always practical to do in the heat of the moment.
In multiplayer, it's typically used more as a defensive weapon than an offensive one. The time it takes to arm makes it hard to use but makes it great for ambushes. They can be thrown now too by holding the ability button down. Take note that only other players will set it off now (civilians will not trigger them).
You'll have to be smart about your placement of the traps. You're playing against human opponents now and can see the bombs on the ground. The ideal placement would be somewhere in front of you between you and possible approach directions. You should try conceal its location by placing it directly underneath an NPC, within debris that's on the ground or behind a wall/divider so pursuers will not see it.