An "element" of a claim is not defined in the law. It's actually a kind of abstraction.
But let's start at the beginning. A patent's protection is defined by the claims. Anything that falls under the scope of any claim infringes that claim. The scope of a claim is all that is described by that claim.
An example might make this clearer.
Claim 1:
A device for moving around humans and/or goods, the device comprising
- at least two wheels
- at least one motor,
the motor beeing designed in such a way that it has at least the power of two horses.
(disclaimer: the last part is somewhat unclear (it defines the problem, not the solution), don't write something like that into a patent claim in real life unless you know what you're doing)
The elements of the claim are "at least two wheels" and "at least one motor". Would a bycicle without a motor infringe this claim? No, it doesn't fall under the wording of the claim as should be rather clear from just reading it. A bycicle is not "a device" as described. So for infringement, all elements need to be present.
But what about "the motor beeing designed in such a way that it has at least the power of two horses", is that an element of the claim? I'd say yes, though you might say it is just part of "a motor". It doesn't really matter, because "element" is not defined. But whatever you call it, if the motor doesn't have the power of two horses or more, you do not infringe the claim.
And "for moving around humans and/or goods" is interpreted as "the device must be able to do that, but not necessarily be used that way". The reason is that the claim describes a device and not a method and if moving around people or goods is something the device could do, it infringes the claim. A (strong) toy car might not infringe though.
How do other claims play into that? There are dependent and independent claims. Independent claims don't depend on other claims, so there is no connection, they are evaluated on their own. Dependent claims are something like claim 2: "the device from claim 1 further including a passenger seat." So without a passenger seat you would still infringe claim 1, but not claim 2. It is read as if it were an independent claim with everything from claim 1 copied into it. Why do we have dependent claims then, if anything that infringes the dependent claim would also infringe the independent claim?
Be wary of optional elements though:
Claim 3:
A device for moving around humans and/or goods, the device comprising
- at least two, preferably exactly 4, wheels or a caterpillar drive
- at least one motor,
the motor beeing designed in such a way that it has at least the power of two horses.
Anything falling under claim 1 also falls under claim 3. Actually claim 3 is more like a combination of claims 1, 4 and 5. Anything infringing any of those infringes claim 3!
4: (strictly speaking this is dependent on 1 because it has a strictly smaller scope/ is completly encompassed by claim 1)
A device for moving around humans and/or goods, the device comprising
- exactly 4 wheels,
- at least one motor,
the motor beeing designed in such a way that it has at least the power of two horses.
5:
A device for moving around humans and/or goods, the device comprising
- a caterpillar drive
- at least one motor,
the motor beeing designed in such a way that it has at least the power of two horses.