Most of the cases I saw where Float was used instead of float (or Boolean instead of boolean, etc.), it was an error... Ie. it served no purpose.

float (or other types starting with a lowercase letter, int, double, boolean, char, byte, etc.) is a so-called primitive type. A kind of raw type, using only the memory needed to store the data. These types break some orthogonality in the language, but are practical because their usage is fast (optimized) and they are economical in memory.

Float (or Integer, Double, Boolean, Character, Byte, etc.) is a so-called wrapper class. It allows to use these types in a OOP environment. Typically, to allow storing them in Java collections like ArrayList or HashMap: these collections can only store and manipulate objects (the type Object), not primitive types.
So you can use an ArrayList<Float> (but not ArrayList<float>).
The cost is that each primitive value is wrapped in an instance of object, adding both some CPU overhead to access the inner type, and lot of memory usage (some 24 additional bytes per value!, IIRC).

So, unless you have a very good reason (the collections being one), use the lowercase version of these types.

Side note: for large collections of primitive values, there are Java libraries like Apache Trove, more efficient in storage term.

Thanks for replying, that's very clear.