BhagavAn bAdarAyaNa says:

yA sandhyA sA jagatsUtiH mAyAtItA hi niShkalA |
IshvarI kevalA shaktiH tattvatrayasamudbhavA ||

sandhyA represents a deity who personifies the jnAna shakti of the Supreme.

ahorAtrasya yaH sandhiH sUryanakShatravarjitaH |
sA tu sandhyA samAkhyAtA munibhiH tattvavAdibhiH ||

The activity or kriyA of worshipping the sandhyA devatA [AdityAkhyAm tejorUpiNIm devatAm] during the sandhi kAla of the day and the night when sUrya and nakShatra maNDala are not completely visible is called
sandhyA [sandhau bhavA kriyA sandhyA]. The same is stated by yAjnavalkya:

sandhau sandhyAmupAsIta nAstage nodgate ravau ||

The lakShaNa of sandhyA is further described as below:

trayANAm chaiva devAnAm brahmAdInAm samAgamaH |
sandhiH sarvasurANAm cha tena sandhyA prakIrtitA ||

sandhyA, based on kAla or time, is referred to by different names:

gAyatrI nAma pUrvAhNe sAvitrI madhyame dine |
sarasvatI cha sAyAhne saiva sandhyA tridhA smR^itA ||

The significance of these three are understood by examining the following verses:

gAyatrI:

pratigrahAdannadoShAt pAtakAdupapAtakAt |
gAyatrI prochyate tasmAdgAyantam trAyate yataH ||

sAvitrI:

savitR^idyotanAt saiva sAvitrI parikIrtitA |
jagataH prasavitrI vA ||

sarasvatI:

vAgrUpatvAt sarasvatI ||

trimUrti svarUpa of the sandhyA traya is also described:

gAyatrI brahmarUpA tu sAvitrI rudrarUpiNI |
sarasvatI viShNurUpA upAsyA rUpabhedataH ||

What should be the attitude of an upAsaka worshipping the sandhyA?

sandhyeti sUryagam brahma sandhAnAdi vidhAnataH |
brahmaivAhamasmIti so.ahamasmIti sA matiH |
bhavedupasakasyeti hyevaM vedavido viduH ||

jIvabrahmAnusandhana is the true purport of sandhyA as sandhyA as described by vyAsa:

nabhinnAm pratipadyeta gAyatrIm brahmaNA saha |
so.ahamasmItyupAsIta vidhinA yena kenachit ||

The same sentiment is echoed elsewhere as:

devo bhUtvA devam yajennAdevo devamarchayet ||