Which groups of Christians hold signs about Jesus or Christianity in public, and why? I often see people standing on the sides of the road holding signs that say things like "Trust Jesus".

Is this something that Christian groups do regularly? Is it specific to a particular denomination? 

What is the intent of doing that? What is the motivation that these people have?
I am not aware of any denominations that display such signs as an official part of their teaching or practices, so the only way of knowing why someone displays such a sign is to ask them.

Beyond that, we can only speculate...

There are two legitimate reasons I can think of to possibly do this:


The most obvious would be simple evangelism.  That is, fullfilment of the great commission, to make disciples.  Many people, I suspect, see such signs and advertisements as a way to spread the good news of Christ's salvation to the world.

Whether such methods are effective evangelism tools is not really on-topic for this question. (And I suspect their effectiveness is very cultural-dependent).
The other legitimate reason I can imagine is praise and worship.  Billboards that read "Jesus is Lord" might be there for the purpose of evangelizing to non-believers, or they might be there simply as a public expression of praise.


And one other possibly legitimate, or possibly illegitimate reason I can imagine:


To earn favor with God. Some Christians might feel it is their duty to do such a thing.  Whether this is legitimate or not may depend on which denomination you ask, as well as specific motives, and is beyond the scope of this question.

Some Christians feel it is a duty to "stand boldly for Christ" in the "culture wars," and might feel this is one way to do that.


And there are many illegitimate reasons I can imagine one might do this.


To look cool. Someone might think waving such a sign makes them look cool.  If not to the general public, perhaps to other members of their church, a love interest, or to themselves.
To look lame. Someone might intentionally put themselves in a situation where they might be ridiculed, so as to be a victim of "religious persecution"... sort of a "martyr mentality."