What does "export grade" cryptography mean? And how is this related to the Logjam attack? I am doing some research on the Logjam attack, and I need help in learning some terms that are new for me.

What does "export grade" cryptography mean? And how is this related to the Logjam attack?
"Export grade" cryptography is a result of The Crypto Wars. Laws were passed in the United States that resulted in the crippling of encryption software that was distributed outside of the United States. This section from wikipedia explains it well enough:


  The longest key size allowed for export without individual license proceedings was 40 bits, so Netscape developed two versions of its web browser. The "U.S. edition" had the full 128-bit strength. The "International Edition" had its effective key length reduced to 40 bits by revealing 88 bits of the key in the SSL protocol. Acquiring the 'U.S. domestic' version turned out to be sufficient hassle that most computer users, even in the U.S., ended up with the 'International' version,[7] whose weak 40-bit encryption could be broken in a matter of days using a single personal computer. A similar situation occurred with Lotus Notes for the same reasons


The 40-bit limit was for symmetric ciphers, where there is no (known) attack better than trying all $2^n$ keys. Asymmetric algorithms like DH and RSA need larger key sizes for the same security; see e.g. How much computing resource is required to brute-force RSA? and Security strength of RSA in relation with the modulus size . At the time 512-bit RSA or DH was rated equivalent to 40-bit symmetric, and thus export of those algorithms was limited to 512 bits. (DSA was rated the same, but was not limited because it is not an encryption algorithm.) This is why weakdh.org states that: 


  The Logjam attack allows a man-in-the-middle attacker to downgrade vulnerable TLS connections to 512-bit export-grade cryptography.


Ultimately, some software was required to be written using key sizes that were understood to be breakable; export grade cryptography refers to this form of an algorithm that uses a reduced and breakable key size. The Logjam attack works by tricking the TLS exchange into using crypto that is weaker and potentially breakable.