つくえの うえに しゃしんが あります / there is a photo on the desk.

あります

means "there is ~" or "~ exists". This is the same function as "います". But, "あります" is for living creature, and "あります" is for things(non-living creatures).

しゃしんが　あります

"しゃしん/photo". So, this means "There is photo.".

つくえの　うえ

"つくえ/desk", "うえ/above". so this means "on the desk". 

つくえの　うえに　しゃしんが　あります

means "there is a photo on the desk."