- a material thing that can be seen and touched.
The term "object" has no special meaning in the rules. 5e D&D's rules use plain English and they try not to infer special meaning beyond the regular English definitions of words.
5e D&D's rules are also exception based: a general rule always applies until a more specific rule applies. This can be applied to all objects. Since "object" is a class that encompasses all things, "Use an Object" is the generic action you take when you want to interact with an object that doesn't already have some other rule for interacting with it.
For example, you wouldn't Use an Object to attack with a weapon, because weapons have a more specific action for their use, the Attack action. You could, however, Use an Object to interact with a weapon in a non-attacking manner, such as drawing it from a sheath. To clarify, the rules do specify that you get one free "object interaction" per turn,
You can also interact with one object or feature of the environment
for free, during either your move or your action. For example, you
could open a door during your move as you stride toward a foe, or you
could draw your weapon as part of the same action you use to attack.
which, as stated, can be used to draw one weapon as part of a move or attack action, but if you were to draw a second weapon in the same turn, that would require the use of the Use an Object action.
Note that this only applies to the generic Use an Object action, and is limited to things you could reasonably do in "less" amount of time than a regular action. Drawing a weapon or opening a door while you move is reasonable. Tying a rope around something is probably not. This will likely vary from DM to DM.
Using a magic item, similarly, has its own rules associated with it and does not normally use the Use an Object action.
Arrows, weapons, armors, and shields are all objects, but if you read the rules for these specific types of objects you will find they all have specific rules for how they are used. To "use" armor (that is, to wear it), you must take time to put it on, and that time varies from armor type to armor type.
Shields are actually a type of armor, and all armors have rules for donning and doffing: it takes one action to don a shield, and 10 minutes to don heavy armor. Donning armor is not Use an Object because it has a specific rule on how to use it.
Arrows have their own rules as well:
Drawing the ammunition from a quiver, case, or other
container is part of the attack (you need a free hand to load a
So when you use an Arrow, you're doing so for free as part of your attack (unless you're not using it to attack with, in which case, you guessed it, it's Use an Object).
All this to say that the Use an Object action is a catch-all that should be used generically when no other rule or action can be taken to interact with or otherwise use an object.