Conjuring doesn't always work
Solution 1:
Is there any message in the top left corner? Is the targeting cross white? Are you targeting a valid location? (Free Space, flat ground)?
Also the conjuration spells have a maximum range.
Also the Atronach perk in the alteration tree, or the Atronach standing stone can cause that problem. The conjuration spell is cast upon oneself, so, you are absorbing a spell that is cast at you. Most people got caught out with this.
Unfortunately for Conjuration mages, the game treats summoning as a spell being cast on yourself, thus the 50% spell absorbtion chance kicks in making your summons 50% likely to not occur. PC Users can avoid this bug by installing the "All in 1 Spell Fixes Mod". Source
Solution 2:
From the Conjuration UESP Wiki article:
Currently a bug exists which causes Summoning spells to fail. As the spell appears to target yourself, any existing Magic Absorb can cause the Atronach or Dremora not to appear, "refunding" the casting cost for no net loss. This can be easily reproduced with a Breton's Dragonskin, Alteration's Atronach perk, or the Atronach Standing Stone. Magic Resist does not appear to have this effect
Install the Unofficial Skyrim Patch (original / Legendary edition - PC) / (Special Edition - PC) / (Xbox One) / (PS4) to fix this bug.
One of its fixes is:
The Absorb Spells effect of the Atronach sign, Atronach perk (Alteration tree) and Breton Dragonskin ability will no longer cause the player's own conjuration spells to fail.