Quarks

A proton is made up of Two Up Quarks and One Down Quark. Whereas a neutron is made of Two Down Quarks and One Up Quark.

Quarks also have an additional property, colour. It is not related to optical colours and is a metaphor (or analogy).
There are 3 kinds of colours: Red, Green and Blue. And there are 3 kinds of anti-colours: Anti-Red, Anti-Green and Anti-Blue.
The colour charges must be conserved by combining the three colours to make neutral white or by colour-anticolour charge pairs.

The quarks are the only particles attracted by the strong force. The Strong Force is mediated by gluons.

Gluons

*Image is for illustration and does not represent the true nature of the gluon.

Gluons carry the colour charge and also interact with each other.
Gluons are virtual particles which are theoretical transient particle that exhibits some of the characteristics of an ordinary particle while having their existence limited by the uncertainty principle.

Red - Anti-Blue
Blue - Anti-Red
Blue - Anti-Green
Green - Anti-Blue
Red - Anti-Green
Blue - Anti-Blue
Green - Anti-Red
Green - Anti-Green

In nucleons (protons and neutrons) there are 3 quarks and few gluons (number can't be predicted)
Both the quarks and gluons have a property known as a colour charge.
Colour charge is a property that some particles have. This field of study is known as Quantum Chromodynamics (QCD).
Gluon's interaction with quarks binds them together.

Gluons are continuously emitted and absorbed by quarks, resulting in a continuous change of colour.
In this case, let us consider a Red-AntiGreen gluon emitted from the down quark.
When this gluon will be absorbed by the green up quarks the Green and AntiGreen charges would annihilate each other and the Red charge is taken up by the 'up quark'.
Since gluons are massless, they move at the speed of light, and a continuous exchange of gluons takes place.
This force is called the STRONG FORCE.
But why is gluon needed in the first place when the nucleon is colour neutral anyways? Because according to the 'quantum field theory', a force carrier is required, also known as a messenger or intermediate particle which is a type of particle that gives rise to forces between other particles. These particles serve as the quanta of a particular kind of physical field.
These fast movements of gluons, form what is known as the 'flux tube'.