The tweak is a service that the encryption method provides for you. What it allows you to do is provide context separation for various encryptions using the same key.
Here's the problem that it is trying to help with: suppose you use the same key to encrypt a number of items; for example, suppose you're encrypting all the items in one column of a database with this key.
This leads to an issue: if the data record corresponding to Alice has a 5 in this field, and the one corresponding to Bob also has a 5 in this field, then both records would have the same encrypted value. Someone looking at the encrypted records won't be able to tell what that common value is, however they know they're the same. And, if Bob knows what his value is, then he knows what Alice's value is.
One obvious way to handle it is to just use a different key for each record. That'd work, but that's a lot of keys to handle and store.
The tweak provides an alternative way to handle it; it changes the mapping between plaintext and ciphertext; however (unlike the key) we don't assume that the attacker doesn't know what it is. In our database example, we might make the tweak the user's name ("Alice" and "Bob"); then, even if Alice's and Bob's encrypted record happen to have the same encrypted value, no one can deduce anything from that (because the mappings from the ciphertext to the plaintext is independent; they might map to the same value, and they might not).
What does this mean for you? Well, that depends on what you're using FE1 for. If you are literally encrypting one value with the key, well, you really don't need it - you can set it to a fixed value (say, the empty string). However, if you are encrypting multiple values with the same key, you might be able to take advantage of it.
One final note: why is this tweak especially important for Format Preserving Encryption? Well, with standard encryption modes, we add a randomization factor (IVs) during encryption (so that, even if you encrypt the same value twice, we'll pick different IVs), and so the encrypted text would look different. However, this randomization necessarily makes the ciphertext larger than the plaintext. With Format Preserving Encryption, we don't have that option; hence we need another way to address this.