Mortgage: This one is simple. It is essentially a loan that a lender gives you that allows you to buy the home. This of course only applies if you are like most of us and do not have all the funds to purchase your desired home outright in cash.
Mortgage rate: The lender will only front you the money for your home if there is something in it for them. So they charge you interest on the amount you borrow from them. The mortgage rate is the rate of interest per annum that you will have to pay for the borrowed funds.
Fixed rate: Most people go with a Fixed rate mortgage. This is the agreed upon rate of interest to be charged on the borrowed funds. This fixed rate does not change over the term of the mortgage. So your interest costs are predictable and the same can be said about your payments.
Variable rate: Variable rate mortgages have an interest rate that can change over the term of the mortgage. Mostly a variable rate will be lower than a fixed rate but that is not always true. A lot of people avoid variable rates because of the uncertainty. Currently interest rates are at historical lows and hence variable rate are low as well. But if the economy improved dramatically say in the next year and rates went up, your mortgage rate would also go up if you went with a Variable rate mortgage.
Open or Closed Mortgage: A open mortgage is one that allows you to pay off the balance of the borrowed funds at any time with no penalties. This provides flexibility in case you need to sell or move to a different lender. A closed mortgage assumes that you will stay with the current mortgage till the end of the term. If you try to leave before hand there will be some "early termination" penalties which typically tend to be around 3 months interest (but could be different). In my experience closed mortgages offer better rates than open and most people tend to opt for those.
Term: The Term of the mortgage is simply the duration of the contract with the lender. It should not be confused with Amortization which refers to the total time you expect to take to pay off the entire loan. The Term comes in various flavours - anywhere from 1 year to 10 year (some can be even longer) but the 3 and 5 year terms tend to be the most popular. At the end of the term, if there is still an outstanding balance on your loan / mortgage, you are free to pay it off without penalties or renew with the lender under new terms or move to a different lender.
Amortization: This is the total anticipated period of time that you expect to take to pay off the mortgage. In most cases it defaults to 25 years. And most people leave it at that. However it does impact your required payments - the longer your Amortization period, the lower your required payments.
Down-payment: The amount of saved funds you must bring to the table for the purchase of your home. Typically 5% is the minimum with some jurisdictions allowing 0% down mortgages as well. With lower down-payments you must also pay mortgage insurance (since the risk of you not being able to pay your mortgage is higher as you have not demonstrated sufficient savings ability) which normally applies if your down-payment is less than
Appraisal: The lender at times will require that your home be appraised since they do not want to loan you more money than the house is worth. If you want to pay more than what the place is worth you have to do that with your own funds.
Pre-payment clauses: Most lenders will allow you some flexibility in making more payments than are required, thus allowing you to pay off your mortgage faster without penalties. Some will allow you to increase your regular payments by a certain percentage while others will allow you to make lump sum payments that do not exceed a certain percentage of the original mortgage amount in any given calendar year.
Payment schedules: Basic mortgage payment schedules require payments once a month. If you get paid twice a month you can split that monthly payment into 2 and pay it each time you get paid. Most lenders offer "accelerated" bi-weekly or weekly payments. For accelerated bi-weekly payments you are basically paying half the required monthly amount every 2 weeks. However since there are 52 weeks in a year, you are making 26 bi-weekly payments each year and thus making 2 extra payments (essentially 13 months worth of payments in 12 months). This only works if your budget allows it but it does allow you to pay off your mortgage a bit faster.
I can't think of anything else at the moment but if I am missing anything, please ask in the comments and I shall add it here.