acertainpov | What is the Force and why is it with me?

"Well, the Force is what gives a Jedi his power. It's an energy field created by all living things. It surrounds us and penetrates us; it binds the galaxy together."

Background

The Force is an all-encompassing, ubiquitous field of energy, a little like qi a little like the Western idea of ether, which penetrates everything in the universe, even space.

Technically it comes in two parts, 'living' and 'cosmic' but we can ignore those parts for now. Yes, there are also midicholarians. These are microscopic beings that have a symbiotic relationship with the Force and with certain living individuals. Don't worry about them either.

Those certain individuals are known as "Force-Sensitives," people who can consciously sense and, with training, manipulate the Force in various ways. In Obi-Wan's youth, young Force-Sensitives were actively sought out, and (with parental permission, but backed by cultural pressure) recruited into the Jedi Order, where they would train to become Jedi. Not all Force-Sensitives were recruited at an age young enough to train, and not all cultures fell into the domain of Jedi cultural dominance, so there are are one or two people throughout the Galaxy who can sense the Force, and even some non-Jedi cultures & untrained individuals who can manipulate the Force, but usually a Force-wielder would be a Jedi or a Sith.

Powers

Force-Users can manipulate the force to give them a massive range of powers rooted in the psychic realms of telepathy (reading and influencing minds), telekinesis (moving objects with ones mind) and Clairvoyence (seeing the future). Every individual user might have different strengths due to training and personal qualities - Obi-Wan for example, doesn't tend to have visions of the future, but if you need someone to placate a pack of savage animals, he's your Jedi.

In fights this gives the Jedi ridiculously fast reflexes (they can see the future!) and the ability to perform ridiculous feats of strength and agility (they can telekinetic their own bodies). They can fight in poor visibility by using their force sensitivity instead of the other five senses, and they can take one hell of a beating because they can mitigate the impact on their bodies. If you're fighting because you've been emotionally manipulated (NOT through technological brainwashing, sadly) they can also calm you the heck down if needed.

In conversation, this looks like a general feeling of safety, warmth and reassurance from Obi-Wan specifically, because he's pretty much projecting this at a very faint subconscious level all the time (your pup can be immune if you want, but it's not strong enough for them to notice.) We're sorry - Obi has no sense of personal space, psychically.

The Jedi Mind Trick

So imagine you're walking along, following a fixed path of for example 'looking for Obi-Wan's droids'. A Jedi-Mind-Trick is the psychic equivalent of gently steering you in a different direction. This has the advantage of being subtle and gentle enough that many people don't notice it, but its effectiveness depends on the individual it's being used on and the force with which it is applied.

Can my pup resist it?

Abso-darned-lutely! The following factors depend on whether the Mind-Trick is effective:

Natural ability (your pup is either psychic or just stubborn as heck)
Species (your pup is a non-human species and you feel like saying that species is immune for whatever reason)
Training (your pup is a goshdarned ninja, or a trained soldier who may or may not run up against psychic arseholes in the course of their work)
Narrative imperative (any or all of the above apply, but it would just be funny for your pup to be affected or not.)

What if the Jedi dials up the power?

First of all, Obi-Wan will not unless the mun communicates it beforehand.

But yes, it can be dialed up to a level above "gentle nudge in this direction." This is noticeable, and it is more effective on people who would resist the above (still not 100% reliable) but it hurts and it's dangerous and Obi-Wan will not be doing it in everyday play.

More Info

The Force on Wookiepedia