The name Ido is Esperanto (and presumably Ido) for "descendant" or "offspring": it is one of the suffixes. For example, hundo 'dog', hundido 'puppy', Izraelido 'Israelite'. It was used as the pseudonym of the proposer of the language, as well as the language itself, to the committee for the Adoption of an International Auxiliary Language meeting in October 1907.

This committee had been set up to adjudicate on rival languages, principal of which were Esperanto and Idiom Neutral, and decide on a single international language. The committee included Louis Couturat, the linguist Otto Jespersen, and the chemist Wilhelm Ostwald. The obvious solution was to use Esperanto, the most popular language, with some improvements. Zamenhof, the inventor of Esperanto, had been happy to take suggestions for improvements, but his followers maintained its inviolacy, and religious wars prevented the adoption of a compromise.

Ido was proposed by Louis de Beaufront, and Louis Couturat, France's foremost Esperantist, took it up as its most enthusiastic supporter. His death in a car crash in 1914, and the conspicuous lack of international goodwill beginning in that year, largely ended the possibility of adopting a unified language.

Ido is more or less what any rational being would come up with once they learnt Esperanto, which is a good idea, but has obvious room for improvement. Ido drops the accented consonants Ĉ Ĝ Ĥ Ĵ Ŝ and Ŭ (none of which are natural to European languages). It is less rigid about root shapes, and is more faithful to familiar Latin roots. It has 16 prefixes and 40 suffixes, compared to Esperanto's 6 and 22, but they are organized more usefully.

One of the most annoying things about Esperanto is that opposites are dispensed with by using the negative prefix mal-. So instead of burdening your memory with separate words for 'hot' and 'cold', 'big' and 'small', 'friend' and 'enemy', you simply create malvarma 'cold', malgranda 'small', malamiko 'enemy'! Ido gives you back comforting terms like mikra 'small', kurta 'short' (not mallonga), apertar 'to open' (not malfermi), and lenta 'slow' (not malrapida).

In Esperanto the direct object has a compulsory accusative ending -n, which is abolished in Ido except for clarity in poetic inversion. The same ending is used adverbially in Esperanto: mi iras Londonon = mi iras al Londono 'I go to London'. This unnecessary baggage is scrapped in Ido.

The Esperanto plural is from Greek (as is the word kaj 'and', for no very good reason: Ido sensibly uses e): granda domo 'big house', grandaj domoj 'big houses' (and accusative grandajn domojn). Ido instead uses the more familiar -i of Italian.

In Esperanto -i out of nowhere was the infinitive: Ido uses the familiar Romance ending -ar.

It has a gender-neutral pronoun lu 's/he'.

Most of the above has been extracted from
http://users.aol.com/idolinguo/
which looks a thoroughly useful site.

Another proposal of a very similar language was called Esperantido, devised by René de Saussure. Another Latin-based language called Interlingua was devised by the mathematician Giuseppe Peano and originally called Latine sine flexione because it was the familiarity of Latin roots stripped of the numbing difficulty and illogicality of the grammar. In The Loom of Language by Lancelot Hogben are quoted parallel examples of the three Esperantic dialects. (I've corrected his mistake, ahem.) The parent Esperanto comes off quite well in this text because it doesn't contain many of the horrors I've mentioned above.

ESPERANTO

Por homo vere civilizita, filosofo aŭ juristo, la kono de la latina lingvo estas dezirebla, sed internacia lingvo estas utila por moderna interkomunikado de landa al alia.

IDO

Por homo vere civilizita, filozofo od yuristo, la konoco di Latina esas dezirinda, ma linguo internaciona esas utila por la komunicado moderna de un lando al altra.

ESPERANTIDO

Por homo vere civilizita, filozofo or yuristo, la kono de la latina linguo estas dezirebla, sed internacia linguo estas utila por moderna komunicado dey un lando al alia.