Airtable is like a spreadsheet and a database
While programs like Excel function only as traditional spreadsheets, Airtable works similarly to both spreadsheets and databases. As a spreadsheet, you can structure information in a grid view with the expected format of columns, rows, and cells. As a database, you can link records to one another to create powerful data links that open up more capabilities for data entry, formula calculations, and more.
Airtable also allows you to view the same data that appears in a grid view in other ways as a calendar, kanban board, form builder, and gallery view.
Airtable formulas reference entire fields, not specific cells
In a spreadsheet, you can put a formula in any cell, and have it reference any other cell in the sheet. Airtable is a relational database so formulas are applied for the entire field (what Airtable calls a column) so that the same formula applies to every record in that field.
Excel
Any specific cell can be referenced in another cell. For example, to identify the source of each purchase in a table, you would write a formula that referenced each cell - like A3 - to check for the type of source it is.
This is the formula used below is:=IF(A3='Online','Web','Store')
References specific cells, like A3.
Airtable
A formula is always applied to an entire field, rather than specific cells. For example, to identify the source of each purchase, you would write one formula to reference the {Purchase Type} field, and the formula will check that field for every record in the table.
This is the formula used below is: IF({Purchase Type}='Online','Web','Store')
NOTE
In Airtable, you don't start a formula off by writing
=. You can instead just start writing the formula.
Airtable formulas work within tables, not across a base
Similar to the above, Airtable formulas by default only reference fields within the same table. However, there are ways to bring over a value from a different table in order to reference it in a formula field (this approach uses linked records and lookup fields, which are covered more in-depth here).
Excel
To reference a record in another table, you have to write specific references to the other table using a format like the following: =IF(Tasks!B1='Home improvements',Tasks!A1,0). You then need to apply that formula to every cell (ensuring you change the cell references for each) where you want to run the formula.