These ten words are taken from a list of the most common Hindi words (courtesy of Hindi Google Group and Resource Center for Indian Language Technology Solutions). Two of them -- 51. गये and 58 उन्होंने -- are still mysterious, i.e., I didn't find a definition for them. I'll have to ask Pradeep and see what he thinks...
Common words in Hindi, numbers 51 through 60:
51. गये ga-ye (verb) plural perfective aspect of जाना, to go
52. कभी ka-bhī (adverb) sometimes; at any time
53. आदि a-di (noun) et cetera
54. लोग log (masculine/feminine/plural noun) people, folk
55. बार bār (masculine noun) 1. times, occasion. 2. gate, door; doorway.
56. यहाँ ya-hāṃ (adverb) 1. here. 2. at
57. दोनों do-noṃ (adverb) the two; both
58. उन्होंने un-hoṃ-ne (pronoun) oblique case of they
59. कार्य kār-ya (masculine noun) 1. action, act; activity. 2. work, task duty.
60. पास pās (adverb) nearby
All translations made with The Oxford Hindi-English Dictionary.
Edit (15 August 2008): Updated with advice from Vinay and Pradeep -- see changes made in Errata, Words 1 to 100.
गये or गए is the past participle form of the verb जाना (to go). So it means went. However, it is the plural/honorofic form. For singular nouns, it will be गया/गई.
E.g. मैं गया. वह गया. बिजली गई. लता गई. लड़कियाँ गईं. वे लोग गए. गाँधी जी गए.
उन्होंने is a bit difficult to explain. It adds 'ने' to 'They' if that makes sense. Understanding the concept of ने in Hindi is often difficult for English speakers. Let me give you some examples if that helps.
उन्होंने पीत्ज़ा नहीं खाया - They did not eat Pizza.
वे ऑरलैंडो गए पर उन्होंने डिजनीलैंड नहीं देखा - They went to Orlando but did not see Disneyland.
Couple of other point regarding your list.
आदि in this frequency list must be in the sense of "et cetera (etc.)", not "beginning". It is used in Hindi in the same way as etc. is used in English. The word in its "beginning" meaning is used rarely and wouldn't be enough to make this word number 53.
बार is commonly used in the 1st listed sense - times (not time). As in तीन बार = three times. The third sense "load" is new to me. I would suspect that it is a mistake for भार, which does mean load or burden.
उन्होंने can also be used to refer to an elderly person. The thing is that, in Hindi, one word can be used in sentence reference to mean many things. I think, I like Vinay's idea of going with sentences instead of words.
It gives more light on the word's usage. The Hindi that I personally learned in High School only pushed upon knowing when to use what and not on which branch of the grammatical hierarchy it stood at. Therefore, when you ask me such general questions, it's a bit difficult to explain - since I only can give examples of how it's used in a sentence.