Clash-of-clans – How does upgrading the traps work

The basic concepts of walls are to protect your Town Hall and/or resources. At your current Town Hall level, upgrading walls may seem expensive, but the higher your Town Hall level, the higher level collectors, barracks, laboratory, and camps you can build. These allow you to attack stronger opponents to steal their resources, by winning battles and increasing your trophies (which makes you face stronger opponents).

Stronger walls and a well planned defensive strategy will prove effective (to some degree, see the bottom of this answer) in slowing down your attackers. While your attacker's troops are trying to get through your walls, your defenses (clan castle, archer tower(s), mortar(s), cannon(s), etc) will be trying to kill them. I would recommend putting your defenses behind your walls.

To answer your question though: Yes, but it depends on the wall breaker's level.
See below:

You can get a lot of information from (and source of the screenshot above) from Clan of Clan's Wiki Page on walls

Also, I mentioned "to some degree" because at higher levels there are troops that can jump over walls(hog riders), fly over walls, and there is a spell that allows all troops to jump over walls!

It is a bit weird at first - the destruction of your base only yields a hunk of your resources being stolen. Repairing your base takes only a few seconds and costs very little.

The overall goal in the game is pretty murky. There are ever-increasing base upgrade goals to be met, which you will gain either by waiting for your own resources to collect, or more quickly by raiding other people's bases. Pride in your town's strength and building levels could thus be considered a major goal of the game.

However, I would argue that the overall goal is to rank highly in the player-vs-player leagues, which require you to amass tons of trophies by successfully attacking other bases or defending your own.