The boot animation is the animation that we see behind the logo when the phone is turned on. If we see that the phone takes time to finish with the animation, first of all we must be calm if it is the first time that we started a newly installed ROM or we have made a wipe data / factory reset, since the first time we have to prepare the whole system operational from scratch.
But if it is not the first time or we have passed the 5 minutes, then habemus problem.
For this, we could try a wipe data / factory reset together with a wipe cache and / or dalvik cache.
If the problem persisted (after waiting for the minutes of rigor to be a first start after the wipe), then something we have done wrong to install a zip, may be incompatible or having been improperly installed. The solution in that situation is to enter the recovery, make all the wipes (as above) and reinstall the ROM.