Interfacing an Altimeter that has Serial Output

9600BPS and 8 data bits, no party and 1 stop bit

The 9600BPS is the speed (baud rate) at which data is sent, i.e. 9,600 bits per second.
Each data character is made up of a number of bits in this case 8 plus a stop bit makes 9, so 9600 means it could send about 1067 characters every second if it sent data continuously.
The stop bit helps tell where one character ends and the next begins.
Parity is a means of helping detect if a character has been corrupted, in this case parity is not being used.

In general you just setup the transmitter and the receiver to use the same settings and you don't need to worry about the bits. Whole characters are written at the transmitter and read at the receiver, the fact that the were sent as bits is normally invisible to you.

Providing the receiver is able to read the characters faster than the transmitter sends them all is well.
Things get more complicated if your receiver is busy doing other things.

Using serial data is relatively slow so you need to think about how fast your altitude will change and that the interface speed will let you take readings fast enough to get the accuracy you want. No problem in a balloon, but worth checking in a rocket.