The two most common types of microphones are Dynamic and Condenser.  There are plenty of articles out there discussing the mechanical differences, but many people simply want to know “What are the differences in sound between them” and “Which one is better for me?”.  This is the most simple way to put it:

Dynamic Microphones are noise-resistant.  They love noise, they can take a lot of noise and you can yell into them all you want.  They pick up very little background noise.

Condenser Microphones are noise-sensitive.  They pick up every little detail.  They pick up every little subtlety and nuance of your voice, but they can also hear your refrigerator downstairs and a car from across the street.

Neither is objectively better or worse than the other, but it depends on how they are being used.  

Here are other differences:

Dynamic Condenser
Drums, Electric Guitar Acoustic Guitar
Common in Radio Stations Common in Recording studios.
Some famous pop artists used Dynamic mics (i.e. Michael Jackson in Thriller). Most singers and rappers you can name recorded on mostly Condenser mics.
Used for live events, on-stage music  performances and political speeches. Condenser mics are avoided for live events because there is too much noise.
Generally, are more durable, survive drops more easily, making them safe for traveling.  Not all Condensers are brittle, but they should be treated with more care.
Generally, $100-500 Price Range Generally, $100-3500 Price Range

How much of an issue is background noise for you?

If the room you are recording in is well treated (i.e. very little to no background noise from outside of the room bleeding in and the walls of the room itself do not echo), then a Condenser microphone will allow you to get a fuller range of sounds out of your voice.

However, if you are recording in an area with noisy roommates/family, cars/dogs/children making noise from noise, Dynamic microphones may be a better choice for you because they will reject a lot of that background noise.

Condensors are certainly an option if you are willing to take some measures to treat the room.  Using blankets and rugs to cover hard surfaces, buying a mic shield or recording in a closet full of clothes is an option to reduce echoes from your voice.  

How loud is your voice?

Other factors will be your voice and the volume of it.  Condenser mics will result in your voice clipping, compressing and distorting if it is too loud, whereas with Dynamic mics, the possibility of you hurting someone’s ear is less.  However, if you have a quiet voice, you may be frustrated with the fact that Dynamic mics put out a low volume into your computer.  Dynamic microphones are power-hungry and require more power to put out more volume.  This problem can be fixed by having an audio interface with a great pre-amp or by buying a mic activator, which does cost additional money.