High / Low Pass Filters from Zero
I will try to be intuitive more than rigorous.
Low Pass Filter means a filter which limits the ability of the output data to change fast (Relative to a parameter called the Low Pass Cut Off Frequency).
Namely it make the signal transient to take longer (Smoother).

How do we do that?
We, make adjacent samples have similar values.

So for applying a Moving Mean Filter (Output is the mean value of few adjacent samples) means we applied a Low Pass Filter.

Another way is Auto Regressive model, which you pointed.
In that mode the output sample is the previous samples with a small addition which again, with proper ratio between the weight of the previous output to the new input means the speed of changes is limited.

This is the intuition.
If your needs are basic this might work (Just apply some weighing with non negative values, Let's say Gaussian Filter).
If you need more advance control you'll need to learn the frequency Representation of the sampled data.