Summation just adds up a bunch of things. Thus,
Summation(1,2,3,4,5) = 1+2+3+4+5 = 15
(note: it always adds: if you want to subtract, do the summation with negative numbers)
It was easy, wasn't it?;)
A vector is an ordered tuple that really just means a bunch of numbers in a specific order. Most often, physics describes the position, strength, speed, etc. .... this is really nothing special, just some ordered numbers, where the order is significant:
v = <1,2,3>
If we are talking about geometry, then this vector is a point in three-dimensional space, where the x coordinate is 1, the y coordinate is 2, and the z coordinate is 3 (see, which was also easy, right)?
In neural networks, a vector is usually a vector of inputs to a neuron, so it really is a list of numerical values. Summing a vector would be nothing more than summing up all the values ββin the vector and resulting in a single number (which can be called a "scalar" value).
(it was thrown and simplified - I'm sure someone else will help me improve it;))
PS. Kudos to you for diving into this material at the high school level! :)