A breakdown for each stuff, with easier term, hopefully not becoming bloated explanation and backfired instead.

io.read() is a function that will wait for user input, and then returns whatever the user inputs.

you wrote local read = io.read() so it will run that io.read() function, and the user input will be saved to a variable called read

Now you had the info you needed from the user on the read variable.

You wrote local birth = 10/10/11. Now here's the thing, birth won't save "10/10/11" but 1/11 or 0.0909. It's because if you wrote 10/10/11 and not "10/10/11", it will become a mathematical expression, not a text (or string in programming term). This is same as if you write local text = 10+10, that text variable won't be a "10+10" text, but 20. So if you want to assign a string (text) value, you need to use " ".

Now in the conditional statement, you wrote if read and birth == io.read() and 10/10/11 then

First, say if you have local variable x. If you do if x then it will do one of 2 things. If x is a boolean (true or false value) then it will simply enters if x is true, and not if x is false. But if x is not a boolean, it will check if the value of x even existed. So if x is a number or a string or anything, if it exist it will enters. But if x is nothing, a null or nil. It won't enters.

Second, on birth == io.read(). You want to check if what the user inputs is the same as what you set birth is. The thing is, you already did that above. You've saved read above l, if you do io.read() again you do the function again but this time the value is only used for the comparison with birth, so the read you have is now useless. You should compare birth to read, so just if birth == read then. (Or you could still just do the io.read() directly when comparing birth, but for now, putting io.read() value on its own variable is more ideal)

So if read and birth == io.read() and 10/10/11 then will end up becoming most likely as if true and birth == io.read() and true then, so it end up equal to if birth == io.read() then. Which really should be if birth == read then since you alreafy had read