The base word is fényképez. Now, if you try to put a -sz at the end, it would leave you with a jumble of sibilants: *fényképezsz, and no one wants to pronounce that. So whenever a verb root ends on such a sound (-c, -cs, -dz, -s, -sz, -z), the conjugation suffix for the single 'you' defaults to -el instead (or to -ol or -öl, depending on the vowel harmony).
- te keresel - you search
- te olvasol - you read
- te főzöl - you cook
- te alszol - you sleep
- te fekszel - you are lying down
And so on.
Where is the plural here? I mean, where is the difference from taking picture and taking pictures?
In Hungarian there is none. Fényképez describes the act of photographing, with no account as to how many pictures are taken. In English you can say either "You are taking pictures" or "You are taking a picture", but it's more common to use the plural if you don't know the exact number of pictures taken.