I am a senior lectuerer in chemistry at a University.
You need to start by considering water, there is a reversable reaction where water splits into H+ and OH-, the H+ concentration in a solution in water defines for most purposes how acidic or alkaline the water solution is.
When something is inside square brackets it means that it is the concentration of a thing in moles per litre.
At 25 oC, the constant (kw) for the splitting up of pure water is 1 x 10^-14, we can write for pure water
[H+][OH-] = kw
As [H+] = [OH-]
[H+] = sqrt (Kw) for pure water
(sqrt = square root)
As you heat up the water Kw becomes larger, so the assumption that neutral means pH 7 only applies at 25 oC for pure water.
pH was defined by some German man as "-log10 [H+]"
There are three defintions for acids, the first two are named after dead Swedish people. For a water based system the Arrhenius defintion of an acid is "a substance which increases the H+ concentration in the water". As the [H+] concentration in a citric acid solution is higher than that of pure water then citric acid meets the Arrhenious definition.
The more useful definition is the Bronsted definition, which defines an acid as a thing which can donate a "proton". The citric acid has three acid groups in the moelcule. We can take a more simple acid such as acetic acid which is in vinigar. This is CH3COOH.
The acetic acid will dissociate when mixed with water to form CH3COO- and H+ ions (charged atoms or charged molecules)
We can write
Ka = [H+][CH3COO-]/[CH3COOH]
For a mixture of water and a moderately strong Bronsted acid such as citric acid we can write
[H+] = sqrt (Ka [CH3COOH])
So by adding acetic acid to the water the concentration of the solvated protons [H+] will go up and pH will go down.
The strength of an acid relates to Ka, the greater the ability of an acid (HA) to dissociate into H+ and A- the higher the strength of the acid. For example hydrogen cyanide (hydrocyanic acid) has a pKa of 9.2 ( -log10 of Ka) which means it is a very weak acid. The pKa of acetic acid is about 4.5 meaning that acetic acid is 50120 times stronger an acid in Ka terms than hydrogen cyanide.
Boric acid is also very weak, it is about as weak as hydrogen cyanide as an acid.
The addition of a base to water has the opposite effect to the addition of an acid. For example the addition of ammonia to water will form a solution which has a lower proton concentration [H+] than water.
For ammonia the pKb is about 4.8.
This means that kb of ammonia is 0.000016
We can write an equation for a base, we write B for a generic base
Kb = [BH+][OH-]/[B]
As [OH-][H+] = Kw
Then as we can write
[OH-] = sqrt (kb [B]) for a mixture of water and the base
We can then write
[H+] = Kw / sqrt (kb [B])
These equations are approximations for moderate concentrations of the acids or bases, they also do not apply for solutions of extremely weak acids like boric acid or hydrogen cyanide in water.
There is a general idea which always applies
Strong acid + Strong base forms weak acid and weak base.
For example
Acetic acid (stronger acid) + ammonia (stronger base) forms ammonium cations (NH4+) which are a weaker acid than acetic acid in terms of Ka, and acetate anions (CH3COO-) which in Kb terms are a weaker base than the ammonia.
I could write a whole 10 hour lecture course on this subject, I am just giving you the basics.
There is a third defintion based on the views of a dead american man called Lewis, this is about electron pairs and I do not think you need to know about this one.
Sadly YourTheTop is not right, an acid does not have to form a solution where the pH is less then 7. For example boric acid and hydrogen cyanide are both acids but their solutions in water are not lower than 7 as they are very weak Bronsted acids.
prepareforharvest has a better understanding of the core concepts