What is connected speech?

When we speak naturally we do not pronounce a word, stop, then say the next word in the sentence. Fluent speech flows with a rhythm and the words bump into each other. To make speech flow smoothly the way we pronounce the end and beginning of some words can change depending on the sounds at the beginning and end of those words.

These changes are described as features of connected speech.

• Connected speech is more than just a string of individual target segments joined together in series, since each segment is liable to influence the segments that surround it. The precise form that these influences take is determined by the particular language in question, and so the phonology of connected speech is part of the phonology of the language that the child has to master . . .."
  (Sara Howard, Bill Wells, and John Local, "Connected Speech." The Handbook of Clinical Linguistics, ed. by Martin J. Ball, Michael R. Perkins, Nicole Muller, and Sara Howard. Blackwell, 2008)

• "Attempting to count the number of words in even a few seconds of a conversation or radio broadcast in an unfamiliar language will quickly demonstrate how difficult that task is because words run together in an utterance of any language.
  Ifwordswereprintedwithoutspacesbetweenthemtheywouldbeprettytoughtoread.
  As you recognize, sorting out the individual words would not be easy. Actually, the task is even more difficult than the run-together words in the printed sentence might suggest because the letters in the sentence above are discrete and separated from one another, but the individual sound segments in spoken words blend together into a continuous stream."
  (Edward Finegan, Language: Its Structure and Use, 6th ed. Wadsworth, 2012)

• "It would be wrong to imagine that the stresspattern is always fixed and unchanging in English words. Stress position may vary for one of two reasons: either as a result of the stress on other words occurring next to the word in question, or because not all speakers agree on the placement of stress in some words. The former case is an aspect of connected speech . . .: the main effect is that the stress on a final-stressed compound tends to move to a preceding syllable and change to secondary stress if the following word begins with a strongly stressed syllable. Thus . . ."

bad-'tempered but a bad-tempered 'teacher
half-'timbered but a half-timbered 'house
heavy-'handed but a heavy-handed 'sentence"
(Peter Roach, English Phonetics and Phonology: A Practical Course, 4th ed. Cambridge University Press, 2009)

• "In fast, connected speech some sounds may be be deleted by the speaker. For example, the sound /t/ may be deleted between the words 'want to,' making the pronunciation of 'want to' sound like "wənnə.' (Note: the symbol ə represents a very short, weak sound.) . . .
  eg. ' . . . I don't wənnə spend too much today.'"
  (Susan Boyer, Understanding Spoken English: A Focus on Everyday Language in Context, Book 1. Boyer Educational Resources, 2003)

• There are some important points to remember about connected speech processes [CSP]:
  - They occur at the edges of words, since this is where words 'meet' in sentences.
  - Importantly, connected speech processes are optional. . . .
  - We can think of them affecting sounds at the phonemic level rather than the allophonic level. When /t/ or /d/ or /h/ is elided, for example, we do not find that a different allophone occurs; we simply find that the phoneme is lost altogether.
  - Because CSPs affect phonemes, they may lead to confusions about meaning . . .
  From: http://grammar.about.com/od/c/g/Connected-Speech.htm 

Source: http://tatiana2-englishproject.blogspot.com/p/blog-page_29.html