Friendship is not the same as Affection, a stat introduced in Generation VI. However, in Let's Go, Pikachu! and Let's Go, Eevee!, the two appear to have been combined, since Affection does not exist in the game, but Pokémon with high friendship gain the same benefits as those that have high affection in other games. {1}
In Let's Go, Pikachu! and Let's Go, Eevee!, benefits that would have been gained from high affection are instead gained by Pokémon with high friendship. Affection, which is not present in the game, appears to have been amalgamated with friendship. {2}
(due to this, I may end up using both terms interchangeably throughout this answer)
The main ways to increase affection are by petting and feeding the Pokémon. These activities are generally limited by the Pokémon's fullness and enjoyment stats as well. {2}
Table displaying the correlation between friendship/affection levels and the points needed to get them
In Pokémon: Let's Go, Pikachu! and Let's Go, Eevee!, friendship is factored into all of a Pokémon's stats, except HP. At maximum friendship, a Pokémon will receive a 10% boost to its stats, before AVs are added in. The friendship multiplier scales directly with the level of friendship, starting from a 0% boost at 0 friendship to receiving the full 10% at 255. {3}
A Pokémon with high levels of affection will gain certain bonuses in battle and will interact with its Trainer in unique ways:
- At affection level 2 and higher, a Pokémon will gain 1.2 times the
normal experience from battles.
- At affection level 3 and higher, a
Pokémon may endure attacks that could otherwise make it faint and
survive with 1 HP (including confusion damage). This can activate
multiple times per turn.
- At affection level 4 and higher, a Pokémon
can sometimes:
- Avoid attacks, even when they have 100% accuracy. This
can activate multiple times per turn.
- Shake off status conditions at
the end of the turn.
- At affection level 5 and higher, a Pokémon's
chance of scoring a critical hit is doubled.
{4}
Your friendship/affection level can be checked by visiting your neighbour's sister in Pallet Town {5} {6} {7}
Sources:
{1}, {2}, {3}, {4}, {5}, {6}, {7}
I hope this helped!