There are lots of ways to encrypt something with a password. Probably the simplest and most secure form of encryption is called a "one time pad." A simple way of performing a basic OTP would work like this:
Let's say you want to encrypt the following message:
The meeting is at noon.
Let's say the "pad" you're going to use is "password". You assign each letter a number corresponding with the letter's position in the alphabet (such as, space=0, A=1, B=2, C=3, and so on). So the values of "The meeting is at noon" would be "20 8 5 0 12 5 5 20 9 14 7 0 9 19 0 1 20 0 14 15 15 14".
Now, to encrypt the phrase, you take the values of your pad ("16 1 19 19 23 15 18 4") and you line them up with your message, so that the first letter of your message (T=20) is lined up with the first letter of your pad (P=16). You then add these two numbers together (36), and if it's more than 26 (which it is), you subtract 27 (all the letters and a space) from the number and you're left with your value (19 in this case). You continue for each letter:
20 + 16 = 36 - 27 = 19
8 + 1 = 9
5 + 19 = 24
0 + 19 = 19
12 + 23 = 35 - 27 = 18
5 + 15 = 20
5 + 18 = 23
20 + 4 = 24
You then repeat your codeword as many times as is needed. Ideally, your "pad" should be longer than your message. In which case, there is no possible way to determine the pad without knowing the message and there's no way to determine the message without knowing the pad. It's literally unbreakable:
9 + 16 = 25
14 + 1 = 15
7 + 19 = 26
0 + 19 = 19
9 + 23 = 32 - 27 = 5
19 + 15 = 34 - 27 = 7
0 + 18 = 18
1 + 4 = 5
20 + 16 = 36 - 27 = 9
0 + 1 = 1
14 + 19 = 33 - 27 = 6
15 + 19 = 34 - 27 = 7
15 + 23 = 38 - 27 = 11
14 + 15 = 29 - 27 = 2
You're left with the following set of numbers:
19 9 24 19 18 20 23 24 25 15 26 19 5 7 18 5 9 1 6 7 11 2
You just convert those back into letters, and you're done!
SIXSRTWXYOZSEGREIAFGKB
In order to decrypt this, you just do the same process backwards. You convert the letters to numbers (and convert the pad to numbers) and you subtract the pad from the encoded phrase. If you get a number less than 0, you just add 27 to that number. You should be left with your original message (if I did all my math correctly).
Computer encryption can work in much the same way. Obviously computers are much faster at encrypting things than people are. There are also various other forms of encryption that do not require long and unique pads in order to operate. Many of these involve very complicated mathematics, so if you're interested, I'll let you do the research yourself. If you want some really interesting stuff, go check out Public-Private Key Cryptography. That's probably the most commonly used method for encryption today. It's full of fancy "features" and is very hard to break.
Hope that clarifies things a bit!